Admin Product Page is broken: «Element with ID 'catalog.product.edit.tab.downloadable.links' already exists»

A related bug: «Argument 1 passed to Magento\Catalog\Block\Adminhtml\Product\Edit\Tab\ChildTab::setTab() must implement interface Magento\Backend\Block\Widget\Tab\TabInterface, instance of Magento\Framework\DataObject given» while opening a simple product in admin.